| 带马尔科夫跳和乘积噪声的随机系统的最优控制 |
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| 引用本文： | 孔淑兰,张召生.带马尔科夫跳和乘积噪声的随机系统的最优控制[J].自动化学报,2012,38(7):1113-1118. |
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| 作者姓名： | 孔淑兰 张召生 |
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| 作者单位： | School of Mathematics Science, Qufu Normal University;Center of Information and Network Technology, Qufu Normal University |
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| 基金项目： | Supported by Outstanding Youth Foundation of Shandong Province (2007BS01014);Nature Science Foundation of Shan-dong Province (ZR2009GM022) |
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| 摘 要： | 讨论了N个选手随机系统的最优控制问题. 设计了无限时间的带有马尔科夫跳和乘积噪声的随机系统的Pareto最优控制器. 应用推广的Lyapunov方法和解随机Riccati代数方程得到了系统的Pareto最优解, 证明了最优控制器是稳定的反馈控制器, 以及对应于最优控制器的反馈增益中的随机Riccati代数方程的解是最小解.
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| 关 键 词： | Pareto解 随机系统 马尔科夫跳 乘积噪声 最小解 |
| 收稿时间： | 2011-1-6 |
| 修稿时间： | 2011-4-4 |
Optimal Control of Stochastic System with Markovian Jumping and Multiplicative Noises |
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| KONG Shu-Lan,ZHANG Zhao-Sheng.Optimal Control of Stochastic System with Markovian Jumping and Multiplicative Noises[J].Acta Automatica Sinica,2012,38(7):1113-1118. |
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| Authors: | KONG Shu-Lan ZHANG Zhao-Sheng |
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| Affiliation: | 1. School of Mathematics Science, Qufu Normal University, Qufu 273165, P. R. China;
2. Center of Information and Network Tech-nology, Qufu Normal University, Qufu 273165, P. R. China |
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| Abstract: | An optimization problem for a stochastic system of N players is presented. An optimal Pareto controller of the stochastic system with Markovian jumping and multiplicative white noises is designed in infinite time horizon. The optimal Pareto solution is obtained by using the generalized Lyapunov equation approach and solving stochastic generalized Riccati algebraic equations (SGRAEs). It is proved that the controller is a stabilizing feedback control and the solution of SGRAEs is minimal associated with the optimal control. |
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| Keywords: | Pareto solution stochastic system Markovian jumping multiplicative noises minimal solution |
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